Question

Find the four second partial derivatives. Observe that the second mixed partials are equal z=x^2+8xy+3y^2

Answer 1

Answer:2,8,8,6

Step-by-step explanation:

$f_x=2x+8y\\f_y=8x+6y\\f_{xx}= 2\\f_{xy}= f_{yx}= 8\\f_{yy}=6$

According to Clairaut's theorem, for most cases, the mixed partial derivatives are equal. In this case, it is.